Fractional-order system identification based on continuous order-distributions

Hartley, Tom T.; Lorenzo, Carl F.

doi:10.1016/s0165-1684(03)00182-8

Cited by 200 publications

(93 citation statements)

References 17 publications

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“…This formula is equivalent to Grunwald-Letnikov  . The classical fractional model [53,58] is taken as the benchmark model (21) for identification in Sections 4.2 and 4.3, as follows:…”

Section: Fractional-order Benchmark Modelmentioning

confidence: 99%

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Genetic Algorithm-Based Identification of Fractional-Order Systems

Zhou

Cao

Chen

2013

Entropy

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Abstract:Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.

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Section: Fractional-order Benchmark Modelmentioning

confidence: 99%

“…Fractional-order system identification is a basic issue of application of fractional calculus [53][54][55][56][57][58]. Several researchers have reported their work on identifying the fractional-order model in the time-domain and frequency-domain.…”

Section: Introductionmentioning

confidence: 99%

Genetic Algorithm-Based Identification of Fractional-Order Systems

Zhou

Cao

Chen

2013

Entropy

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“…But appropriate methods for the analytical or numerical calculations of fractional-order differential equations (FODE) are needed in such cases [10,11,12,13,14] and also methods for the identification of such systems in time domain or in frequency domain [21,22,23,24,25,26,27,28,29,30,31,32].…”

Section: Introductionmentioning

confidence: 99%

Identification of Fractional-Order Dynamical Systems Based on Nonlinear Function Optimization

'ak¹,

Gonzalez²,

'ak³

et al. 2013

Int. J. of Pure and Appl. Math.

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In general, real objects are fractional-order systems and also dynamical processes taking place in them are fractional-order processes, although in some types of systems the order is very close to an integer order. So we consider dynamical system whose mathematical description is a differential equation in which the orders of derivatives can be real numbers. With regard to this, in the task of identification, it is necessary to consider also the fractional order of the dynamical system. In this paper we give suitable numerical solutions of differential equations of this type and subsequently an experimental method of identification in the time domain is given. We will concentrate mainly on the identification of parameters, including the orders of derivatives, for a chosen structure of the dynamical model of the system. Under mentioned assump- tions, we would obtain a system of nonlinear equations to identify the system. More suitable than to solve the system of nonlinear equations is to formulate the identification task as an optimization problem for nonlinear function minimization. As a criterion we have considered the sum of squares of the vertical deviations of experimental and theoretical data and the sum of squares of the corresponding orthogonal distances. The verification was performed on systems with known parameters and also on a laboratory object.

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“…The last few decades have witnessed considerable progress in the c 2011 Diogenes Co., Sofia pp. 436-453 , DOI: 10.2478/s13540-011-0027-3 study of real physical systems dynamical described by fractional-order calculus equations [11], it is found that fractional calculus is an adequate tool for the study of so called "anomalous" social and physical behaviors, in reflecting the non-local, frequency-and history-dependent properties of these phenomena [7,20]. For more knowledge of theory and applications on fractional calculus, please refer to [4,2,12,15,30,31].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of fractional-order systems with double noncommensurate orders for matrix case

Jiao

Chen

2011

fcaa

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Bounded-input bounded-output stability issues for fractional-order linear time invariant (LTI) system with double noncommensurate orders for the matrix case have been established in this paper. Sufficient and necessary condition of stability is given, and a simple algorithm to test the stability for this kind of fractional-order systems is presented. Based on the numerical inverse Laplace transform technique, time-domain responses for fractional-order system with double noncommensurate orders are shown in numerical examples to illustrate the proposed results.MSC 2010 : Primary 26A33; Secondary 33E12, 34A08, 34K37, 35R11, 60G22Key Words and Phrases: fractional-order systems, double noncommensurate orders, bounded-input bounded-output stability, numerical inverse Laplace transform technique

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Fractional-order system identification based on continuous order-distributions

Cited by 200 publications

References 17 publications

Genetic Algorithm-Based Identification of Fractional-Order Systems

Genetic Algorithm-Based Identification of Fractional-Order Systems

Identification of Fractional-Order Dynamical Systems Based on Nonlinear Function Optimization

Stability analysis of fractional-order systems with double noncommensurate orders for matrix case

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